We show in this letter how to extend the Hamiltonian analysis of the asymptotic structure of gravity to cover supergravity. It turns out that both sets of parity conditions - those of [1]} and those of [2]}, [3]} - admit a supersymmetric extension of the BMS\(_4\)  algebra with an infinite number of fermionic generators, but that those of [1]}, on which we shall focus here, lead to a superalgebra with a richer structure that those of [2]}, [3]}. In particular, the graded brackets between the fermionic generators yield all BMS\(_4\)  supertranslations and not just the ordinary spacetime translations. The fermionic generators may be considered for that reason as being the “square roots” of the BMS\(_4\)  supertranslation generators.
